The biplate that consists of two single wave plates made from birefringent materials with their fast axes oriented perpendicular to each other is one of the most commonly used retarders in many optical systems. The internal alignment of the optical axes of the two single wave plates is a key procedure in the fabrication and application of a biplate to reduce the spurious artifacts of oscillations in polarization properties due to the misalignment error and to improve the accuracy and precision of the systems using such biplates. In this paper, we propose a method to accurately align the axes of an arbitrary biplate by minimizing the oscillations in the characteristic parameter spectra of the biplate detected by a spectroscopic Mueller matrix ellipsometer (MME). We derived analytical relations between the characteristic parameters and the misalignment error in the biplate, which helps us to analyze the sensitivity of the characteristic parameters to the misalignment error and to evaluate the alignment accuracy quantitatively. Experimental results performed on a house-developed MME demonstrate that the alignment accuracy of the proposed method is better than 0.01° in aligning the optical axes of a quartz biplate.